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Inverse scattering problem for the Schrödinger equation with magnetic potential at a fixed energy. (English) Zbl 0843.35133
Authors’ abstract: “We consider the Schrödinger operator in $\bbfR^n$, $n\ge 3$, with electric and magnetic potentials which decay exponentially as $|x|\to \infty$. We show that the scattering amplitude at fixed positive energy determines the electric potential and the magnetic field”.

35R30Inverse problems for PDE
81U40Inverse scattering problems (quantum theory)
35P25Scattering theory (PDE)
Full Text: DOI
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[5] Nakamura, G., Sun, Z., Uhlmann, G.: Global Identifiability for an Inverse Problem for the Schrödinger Equation in a Magnetic Field. Preprint · Zbl 0843.35134
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[7] Novikov, R.G.: The inverse scattering problem on a fixed energy level for the two-dimensional Schrödinger operator. J. Funct. Anal.103, 409--463 (1992) · Zbl 0762.35077 · doi:10.1016/0022-1236(92)90127-5
[8] Novikov, R.G.: The inverse scattering problem at fixed energy for the three-dimensional Schrödinger equation with an exponentially decreasing potential. Commun. Math. Phys.161, 569--595 (1994) · Zbl 0803.35166 · doi:10.1007/BF02101933
[9] Sun, Z.: An inverse boundary value problem for Schrödinger operator with vector potentials. Trans of AMS338 (2), 953--969 (1993) · Zbl 0795.35143 · doi:10.2307/2154438